Sensitivity Analysis in Parametric Convex Vector Optimization

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2024-09-18 DOI:10.1007/s11228-024-00733-3

Duong Thi Viet An, Le Thanh Tung

引用次数: 0

Abstract

In this paper, sensitivity analysis of the efficient sets in parametric convex vector optimization is considered. Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps. We establish the formulas for computing the Fréchet coderivative of the profile of the above three kinds of perturbation maps. Because of the convexity assumptions, the conditions set are fairly simple if compared to those in the general case. In addition, our conditions are stated directly on the data of the problem. It is worth emphasizing that our approach is based on convex analysis tools which are different from those in the general case.

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参数凸向量优化中的灵敏度分析

本文考虑了参数凸向量优化中有效集的灵敏度分析。也就是说，扰动映射、弱扰动映射和适当扰动映射被定义为集值映射。我们建立了计算上述三种扰动图轮廓的弗雷谢特编码求导公式。由于凸性假设，与一般情况相比，所设定的条件相当简单。此外，我们的条件是直接根据问题的数据提出的。值得强调的是，我们的方法是基于凸分析工具，这与一般情况下的工具不同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.